DAVIES, T.H. ... et al, 2006. Dual coupling networks. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 220(8), pp.1237-1247.
Using dual graphs and dual couplings, it is shown how the dual of a coupling network
can be found. The actions that can exist within an overconstrained coupling network are shown
to be geometrically identical to the motions that can occur within the dual of that coupling
network. Most useful coupling networks, such as mechanisms within machinery, are both overconstrained
and underconstrained. Motions of machine parts attributable to underconstraint
can be seen thereby making the motions easy to imagine from a drawing. Conversely, internal
actions attributable to overconstraint cannot be seen and so are difficult to imagine. Such
actions could result in fatigue failure. Thus one possible benefit of creating the dual of a coupling
network is that internal actions hidden within it become recognisable motions of bodies in
its dual. This article could lead to a better awareness of overconstraint and its dangers.